Mathematics - Quadratic Equation Question with Solution | TestHub

If the quadratic equation $p{x}^2+qx+r=0$ has no real roots, its discriminant must be negative. So, $D=q^2-4pr<0$. This implies $q^2<4pr$. Since $q^2\ge 0$, it must be that $4pr>0$, which means $pr>0$. This condition implies that $p$ and $r$ must have the same sign.